You are right, we disagree about what PoS means...

I believe I use it in the original meaning from around 2010, but I might be mistaken.

I do fail to see how the current use of the term PoS guarantees anything against a cartel of bad actors...

With "Proof of Stake" to mean a consensus system, are you saying the Ethereum Proof of Stake implementation doesn't do anything to guarantee against a cartel of bad actors?

My understanding is "slashing" may be one such mechanism. This is where staked funds are taken away from bad actors. ie if you propose a block with bad transactions, the 32 ETH you have staked will be reduced by some fraction as punishment. When your stake is slashed down to 16 ETH you are booted from the system. So that us a clear punishment against a bad actor, though I'm not sure what a cartel means i this case. Perhaps you know about this already however.

A cartel is a group of bad actors working together with full, but hidden coordination....

Proof of Work is not resilient to a sufficiently large 'cartel' either in this case. If your cartel is 51% of bitcoin miners by hashrate, they can agree to let each other spend their bitcoin twice. Of course, this is sufficiently hard to do with proof of work, as with proof of stake, as to make it infeasable, perhaps even moreso with proof of stake.

As an example with bitcoin specifically, it would probably be cheaper to buy enough mining hardware to constitute 51% of the bitcoin network than it would be to buy 51% of all bitcoin.

Of course, both would be very expensive endeavors.